Preheat oven to 325°F. Coat a 9- x 5-inch loaf pan with baking spray. Line loaf pan with parchment paper; coat with baking spray.
Beat granulated sugar and butter with a stand mixer fitted with a paddle attachment on medium-high speed until very fluffy, 5 to 6 minutes, stopping to scrape sides of bowl. Add eggs, one at a time, beating well on medium speed after each addition.
Stir together sifted flour, salt, and baking powder. Gradually add flour mixture to butter mixture on low speed, alternately with milk and 1/4 cup of the lemon juice, beginning and ending with flour mixture, beating just until combined after each addition. Stir in 1 tablespoon lemon zest. Beat on high speed until fluffy, about 1 minute. Spoon batter into prepared loaf pan.
Bake in preheated oven until a wooden pick inserted in center of cake comes out clean, about 1 hour, 5 minutes. Remove from oven and let stand for 10 minutes. Remove cake from loaf pan and let cool completely on a wire rack, about 2 hours.
Place powdered sugar and remaining 1 tablespoon lemon zest in a medium bowl. Whisk in remaining 4 to 5 tablespoons lemon juice as needed to reach desired consistency until smooth. Drizzle over cooled cake.